Question

因式分解（x³+y³）²-9x²y²（x+y）²

Answer 1

原式

=(x³+y³)²-[3xy(x+y)]²

=[(x³+y³)+3xy(x+y)][(x³+y³)-3xy(x+y)]

=[(x+y)(x²-xy+y²)+3xy(x+y)][(x+y)(x²-xy+y²)-3xy(x+y)]

=(x+y)(x²-xy+y²+3xy)(x+y)(x²-xy+y²-3xy)

=(x+y)²(x²+2xy+y²)(x²-4xy+y²)

=(x+y)^4(x²-4xy+y²)